Flexural rigidity

About: Flexural rigidity is a research topic. Over the lifetime, 3829 publications have been published within this topic receiving 56780 citations.

Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach

Abstract: The free vibration of axially functionally graded (FG) non-uniform beams with different boundary conditions is studied using Differential Transformation (DT) based Dynamic Stiffness approach. This method is capable of modeling any beam (Timoshenko or Euler, centrifugally stiffened or not) whose cross sectional area, moment of Inertia and material properties vary along the beam. The effectiveness of the method is confirmed by comparing the present results with existing closed form solutions and numerical results. In FG beams, flexural rigidity and mass density may take majority of functions including polynomials, trigonometric and exponential functions (converted to polynomial expressions). DT based Dynamic stiffness approach is proved to be a versatile and simple approach compared to many other methods already proposed.

Effective-medium theory of a filamentous triangular lattice.

Abstract: We present an effective-medium theory that includes bending as well as stretching forces, and we use it to calculate the mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability $p$. We find a rigidity threshold ${p}_{\mathrm{b}}$ which has the same value for all positive bending rigidity and a crossover characterizing bending, stretching, and bend-stretch coupled elastic regimes controlled by the central-force rigidity percolation point at ${p}_{\mathrm{CF}}\ensuremath{\simeq}2/3$ of the lattice when fiber bending rigidity vanishes.

Diagnostic apparatus and methods for a coriolis flow meter

Abstract: A method for validating a flow calibration factor of a flow meter is provided according to an embodiment of the invention. The method for validating a flow calibration factor of a flow meter comprises determining an initial flexural stiffness of a component of the flow meter. The method for validating a flow calibration factor of a flow meter includes determining a current flexural stiffness of the component. The method for validating a flow calibration factor of a flow meter further includes comparing the initial flexural stiffness to the current flexural stiffness. The method for validating a flow calibration factor of a flow meter further includes detecting a calibration error condition responsive to comparing the initial flexural stiffness to the current flexural stiffness.

Elastic response of carbon nanotube forests to aerodynamic stresses.

Abstract: The ability to determine static and (hydro)dynamic properties of carbon nanotubes (CNTs) is crucial for many applications. While their static properties (e.g., solubility and wettability) are fairly well understood, their mechanical responses (e.g., deflection under shear) to ambient fluid flow are to a large extent unknown. We analyze the elastic response of single-walled CNT forests, attached to the bottom wall of a channel, to the aerodynamic loading exerted by both laminar and turbulent flows. Our analysis yields analytical expressions for velocity distributions, the drag coefficient, and bending profiles of individual CNTs. This enables us to determine flexural rigidity of CNTs in wind-tunnel experiments. The model predictions agree with laboratory experiments for a large range of channel velocities.

Dependency of the tensile modulus on transverse dimensions, water potential, and cell number of pith parenchyma

Abstract: Uniaxial tensile tests of solid and hollow cylindrical plugs of pith parenchyma from potato tubers indicate the tensile modulus of elasticity, E, can vary significantly as a function of tissue transverse area and water potential. E increases from 1.2 to 19 MPa as *, changes from -1.4 to -0.4 MPa. E increases from 5 to 19 MPa as transverse area of solid tissue sample increases from 0.2 to 2.5 cm2. Variations in E accompanying changes in transverse area appear to be related to cell number along the radii of plugs. Hollow cylindrical plugs for which wall thickness is maintained but total tissue area is changed show constant values of E. It is suggested that shear stresses within tissue samples influence E and are dependent upon cell number and tissue water content. Material with these properties would be a "poor choice" for constructing plant organs experiencing repeated stress and periodic dehydration. However, ground tissue may act as a buffer against localized ovaling of stem and leaf cross sections under loading. PLANTS MUST BEAR their own weight during vertical growth, as well as the stresses induced by dynamic loading caused by wind and other forces (Fraser, 1962; Wainwright et al., 1976; Niklas, 1986). The extent to which they accomodate these stresses depends in large part upon the flexural rigidity of supporting tissues. Flexural rigidity is defined as the product of two parameters: the second moment of inertia (I) and the modulus of elasticity (E) (Timoshenko and Goodier, 1951; Gordon, 1978; cf. Silk, Wang, and Cleland, 1982). The second moment of inertia is a measure of the distribution of mass around the longitudinal axis of a structure and is dependent upon transverse geometry. E is defined as the proportionality constant relating stress to strain within the elastic range of a linearly elastic material (Sokolnikoff, 1956), and is a measure of material property. Theoretical treatments of inorganic, geometrically simple structures usually consider the values of E and I as constant. However, the value of E is known to vary in plant tissues as a function of water content (Robichaux, Holsinger, and Morse, 1986; Niklas and O'Rourke, 1987). Similarly, the transverse area of stems and leaves, and hence I, can vary due to the I Received for publication 1 April 1987; revision accepted 16 December 1987. The author wishes to thank two anonymous reviewers whose suggestions led to substantial improvements on the original version of this paper. This research was supported in part by NSF Grant BSR8320272. allometry of growth, or as a result of bending or injury (McMahon and Kronauer, 1976). Falk, Hertz, and Virgin (1958) presented data indicating the value of E, as measured by tensile stress, increases as the transverse area of solid cylinders of pith parenchyma from potato tubers increases. This phenomenon was most pronounced for tissue samples with a relatively high turgor pressure and was less evident in dehydrated tissue samples. Falk et al. (1958) speculated that the degree to which neighboring cells could move in response to shear stresses within the tissue was influenced by tissue water content and by the number of adjoining cells. Later studies ofithe mechanical properties of potato tubers, for example Finney and Hall (1967), failed to report a relationship between transverse area (hence cell number) and E, or involved corrections in area to accomodate inferred tissue damage (Somers, 1966). Consequently, the issue raised by Falk et al. (1958) has been largely ignored or forgotten. This paper repeats the experiments of Falk et al. (1958) and presents data on the relationships among the values of E, water potential and the wall thickness of hollow cylinders of pith parenchyma. In hollow cylinders, wall thickness can be maintained (thereby holding the number of cells in radial transect relatively constant) while varying the radius of the cylinder and hence the total cross-sectional area of tissue subjected to tension. In tandem, the results from solid and hollow cylinders indicate E changes as a function of cell number in